Using nitrogen instead of straight air, you save 3.4% in weight of gas. Assuming the tyre itself weighs about 8kg, and contains about 0.01 cubic metres of air at 2 atmospheres, the overall weight saving, not counting the metal of the wheel, is about 0.01%. Nitrogen is more thermally conductive than air- about 1% more conductive.

I think my idea for a scam is better- all those people buying hugely expensive oxygen free copper cables for hifi, then leaving them out in the air! I'll supply protective jackets filled with inert- no noble gases. The mix of gases is tuned to the room's characteristics, and the listener's preferences, by Feng Shui, dowsing, Pilates and homeopathy. Argon for heavier bass, helium for treble. Krypton for Seltic music, heavy metal fans get radon. $50 a fill that lasts a full 3 months before it needs doing again, it's a snip!